Work

The stochastic energy-Casimir method

Year: 2018

Type: article

Abstract: In this paper, we extend the energy-Casimir stability method for deterministic Lie–Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems.

Source: Comptes Rendus Mécanique

DOI: 10.1016/j.crme.2018.01.003

Authors: Alexis Arnaudon, Nader Ganaba, Darryl D. Holm

Institution: Imperial College London

Language: French

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: bronze

Funders: Imperial College London, Engineering and Physical Sciences Research Council, H2020 European Research Council